Our future objectives are twofold: (i) to improve the time-evolution
algorithm, and (ii) to employ the method for the study of other
problems in molecular electronics and phononics. By improving the
methodology, we would like to extend the usability of our method to
difficult parameter regimes (strong coupling), e.g., by developing
an equation-of-motion for the memory function [1]}, [2]}.
This will also allow us to simulate more feasibly the dynamics of an
\(n-\) level subsystem. Another related objective is the study of heat current characteristics in the spin-boson molecular junction
[3]}, . The single-bath spin-boson model displays a
rich dynamics with a complex phase diagram. Similarly, we expect
that the nonequilibrium version, with two harmonic baths of
different temperatures coupled to the TLS, will show complex
behavior for its heat current- temperature characteristics. Recent
results, obtained using an extension of the noninteracting blip
approximation to the nonequilibrium regime [4]},
demonstrate rich behavior. Other problems that could be directed
with our method include plexcitonics systems, as the coupling
between surface plasmons and molecular excitons
should be treated beyond the perturbative regime
[5]}. Finally, we have discussed the calculation of
reduced density matrix and currents in the path-integral framework.
It is of interest to generalize these expressions and gain higher
order cumulants, for the study of current, noise, and fluctuation
relations in many-body out-of-equilibrium systems.
